Potential energy of hydrogen atom motion on Pd(111) surface and in subsurface: A first
principles calculation
Nobuki Ozawa, Tanglaw A. Roman, Hiroshi Nakanishi, Hideaki Kasai, Nelson B. Arboleda, and Wilson Agerico Diño
Citation: Journal of Applied Physics 101, 123530 (2007); doi: 10.1063/1.2749295 View online: https://doi.org/10.1063/1.2749295
View Table of Contents: http://aip.scitation.org/toc/jap/101/12 Published by the American Institute of Physics
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Adsorption of hydrogen on the surface and sub-surface of Cu(111)
Potential energy of hydrogen atom motion on Pd
„111… surface
and in subsurface: A first principles calculation
Nobuki Ozawa, Tanglaw A. Roman, Hiroshi Nakanishi, and Hideaki Kasaia兲
Division of Precision Science & Technology and Applied Physics, Osaka University, Suita, Osaka, 565-0871, Japan
Nelson B. Arboleda, Jr.
Division of Precision Science and Technology, Osaka University, Suita, Osaka, 565-0871, Japan; Department of Applied Physics, Osaka University, Suita, Osaka 565-0871, Japan;
and Physics Department, De La Salle University, 2401 Taft Avenue, Manila 1004, Philippines Wilson Agerico Diño
Center for the Promotion of Research on Nanoscience and Nanotechnology, Osaka University, Toyonaka, Osaka 560-8531, Japan; Department of Physics, Osaka University, Toyonaka, Osaka 560-0043,
Japan; and Physics Department, De La Salle University, 2401 Taft Avenue, Manila 1004, Philippines 共Received 14 October 2006; accepted 11 May 2007; published online 28 June 2007兲
We calculate the adiabatic potential energy for hydrogen atom motion on a Pd共111兲 surface and in a subsurface within the framework of the density functional theory in order to understand the diffusion mechanism of a hydrogen atom from the Pd共111兲 surface to the subsurface. According to the calculated adiabatic potential energy surface for the hydrogen atom motion up to the third atom layer, an effective diffusion path of the hydrogen atom into the Pd bulk starts from the fcc hollow site on the Pd共111兲 surface. Moreover, the diffusion path passes through the octahedral site between the first and the second Pd atom layers, the tetrahedral site beneath a Pd atom of the first layer or above the Pd atom of the third layer, and the octahedral site between the second and third layer. © 2007 American Institute of Physics.关DOI:10.1063/1.2749295兴
I. INTRODUCTION
For years, the production of hydrogen in large quantity by a reforming reaction of fossil fuel performed by high temperature ionization with water or oxygen has been impor-tant for the fuel cell energy system.1However, carbon mon-oxides and sulfur contents are also generated as impurities simultaneously with hydrogen in the high temperature ion-ization. These impurities lower the power generation effi-ciency of fuel cells by poisoning the electrode catalysts.2As a consequence, people have paid their attention to technol-ogy in which hydrogen-permeable films such as Pd thin films separate the pure hydrogen fuel and the impurities to prevent the poisoning of the electrode.3,4While a Pd metal has high abilities of adsorption and diffusion for hydrogen, it is easy to cause hydrogen embrittlement due to the high hydrogen storage ability of the Pd metal. Moreover, alternative mate-rials need to be developed due to the expensive Pd metal. In order to solve these problems of the Pd metal, it is important to clarify the behaviors of hydrogen molecules and atoms on the Pd surface and in the subsurface in detail. Hence, studies about the behaviors of the hydrogen on the hydrogen-Pd sys-tem, such as the dissociative adsorption of hydrogen mol-ecule and the diffusion, absorption, and associative desorp-tion of hydrogen atom, have been carried out through experimental and theoretical methods for a long time.5–15 Al-though it is necessary to consider quantum effects in inves-tigating the behavior of the hydrogen atom on solid surfaces due to the small mass of the hydrogen, these depend
consid-erably on the breadth共or curvature兲 of the adiabatic potential energy surface for the hydrogen atom motion.16–27 In this article, we calculate the potential energy for the interaction of the hydrogen atom with Pd共111兲 up to the third subsurface atom layer based on the density functional theory. Although there are no calculations made on the quantum states for the hydrogen atom motion, improvements on the typical features of the behaviors of the hydrogen atom can be obtained from the characters of the potential energy surface共PES兲 that we calculated. Also, in order to understand how the hydrogen atom behaves after adsorbing on the Pd共111兲 surface, we comment on the diffusion mechanism of the hydrogen atom from the Pd共111兲 surface to the subsurface 共from the first atom layer to the third atom layer兲 according to characters of the obtained PES.
This paper is organized as follows. In Sec. II, some de-tails for the calculation methods of the adiabatic PES for the hydrogen atom motion are given. Our calculation results of the PES are shown and the characters of the PES are dis-cussed based on these results in Sec. III. Finally, we summa-rize the main points of this paper in Sec. IV.
II. THEORY
A slab structure is used for calculating the adiabatic po-tential energy surface describing how the hydrogen atom mo-tion is affected by the Pd共111兲 surface as a funcmo-tion of the atom position on the Pd共111兲 surface and in the Pd共111兲 sub-surface. The calculations in this study are based on the den-sity functional theory, as implemented in the total energy calculation code using plane waves and pseudopotentials,
a兲Electronic mail: [email protected]
DACAPO.28Here, the energy origin of the potential energy is obtained from the sum of the total energy of an isolated slab and that of an isolated hydrogen atom. The plane-wave set is cut off at kinetic energies of 60 Ry. The surface Brillouin zone is sampled with a Monkhorst-Pack29grid of 4⫻4⫻1 k points. With these cutoff energy and point sampling of the surface Brillouin zone, convergences of the total energy cal-culations are confirmed. The generalized gradient approximation30 is adopted for the exchange correlation en-ergy. In our calculation, periodically repeated slabs of five atomic layers are used with a 2⫻2 unit cell, or with a 0.25 ML 共monolayer兲 hydrogen atom coverage. Table I shows how this number of layers is adequate for accuracy of the calculated potential energies at the high symmetry sites on the surface. Here, it is shown that variations in the potential energy values on the three, four, and five atom layers are very little. We were also able to verify that even for three atom layers beneath the hydrogen atom, the interaction be-tween the hydrogen atom and the Pd surface already con-verges. Thus, the five atomic layers are chosen as the ad-equate number of Pd atom layers in our calculation of the potential energy for the hydrogen atom motion up to the third atom layer. A vacuum of a size equivalent to six atomic layers separates adjacent slabs, and all atom positions of the slab are fixed. All calculations in this study have been per-formed with the lattice constant of 3.99 Å calculated for bulk Pd共experimental value31is 3.89 Å兲. Here, the origin of the z coordinate in the direction perpendicular to the surface is set at the first atom layer, and the regions of positive and nega-tive z correspond to the vacuum and subsurface regions, re-spectively. The potential energy calculations are performed
at grid points of a total number of 8⫻8⫻28. The 8⫻8 grid points are located in the plane parallel to the surface within the unit cell while the 28 grid points are located in the direc-tion perpendicular to the surface from the 2.0 to − 4.75 Å at an interval of 0.25 Å. To obtain the smooth PES for the hydrogen atom motion on the Pd共111兲 surface and in the subsurface, the calculated potential energies are interpolated in the directions parallel and perpendicular to the surface by the three-dimensional cubic spline functions.
III. RESULTS AND DISCUSSION
Figure1 shows the calculated adiabatic potential energy curves共PECs兲 for the hydrogen atom motion on the Pd共111兲 surface and in the subsurface. In each curve, the potential energy of the H–Pd system is plotted as a function of the hydrogen atom’s z coordinate along the surface normal through the surface top, fcc hollow, hcp hollow, or bridge site. Based on Fig. 1, the potential energy takes values of −2.92 eV at the fcc hollow site, −2.88 eV at the hcp hollow site, −2.55 共−2.45兲 eV at the octahedral 共OH兲 site between the first and second共second and third兲 atom layers 关first OH site 共second OH site兲兴, −2.38 共−2.25兲 eV at the tetrahedral 共TH兲 site above the second 共third兲 layer Pd atom 关first TH1 site共second TH1 site兲兴, and −2.30 共−2.23兲 eV at the tetrahe-dral site beneath the first共second兲 layer Pd atom 关first TH2 site共second TH2 site兲兴. These sites are described specifically in Fig.2. The PECs indicate that the global minimum of the potential energy can be observed at the fcc hollow site on the surface, while local minima can be observed at the OH and TH sites in the subsurface. Moreover, the OH sites are found to be lower in energy than the TH sites. Other periodic den-sity functional theory 共DFT兲 calculations give potential en-ergy values of −0.51 and −0.45 eV at the fcc and hcp hollow sites at a 1.0 ML coverage共Dong et al.6兲. Moreover, Lovvik
et al.7suggested values of −0.44 and −0.41 eV at the fcc and hcp hollow sites at a 0.25 ML coverage and 0.02 eV at the first OH site at a 0.33 ML coverage. Our calculated potential energies are −0.52, −0.48, and −0.15 eV at the fcc hollow, hcp hollow, and first OH sites at a 0.25 ML coverage. These values were obtained using the sum of the total energy of the
TABLE I. The calculated adiabatic potential energy for the hydrogen atom motion at the symmetry sites on Pd共111兲 for different number of atomic layers. All values are in eV.
Three layers Four layers Five layers
fcc hollow −2.9651 −2.9213 −2.9027 hcp hollow −2.9371 −2.8774 −2.8623 Bridge −2.8423 −2.7662 −2.7514
FIG. 1. Calculated adiabatic potential energy E of a hydrogen atom on the Pd共111兲 surface and in the subsurface as a function of the surface perpendicular coordinate, passing through specific sites on the surface as well as on the bridge sites in the second and third layers. The vertical axis corresponds to the potential energy E共eV兲 and the horizontal axis corresponds to the z coordinate of the hydrogen atom. Here, the energy origin of the potential energy is the sum of the total energy of the isolated slab and that of the isolated hydrogen atom. The first, second, and third bridge sites correspond to the bridge sites on the first, second, and third atom layer, respectively.
isolated slab and that of an isolated hydrogen molecule 共a half value of the binding energy of the hydrogen molecule is 2.40 eV兲 as reference. Our results are fairly in agreement with the other calculated results.
Isosurfaces of the PES at various energies are presented in Fig. 3. Figure3共a兲shows the isosurface at E = −2.91 eV which corresponds to the isosurface with the lowest energy that illustrates the localized hydrogen atom motion at the fcc hollow site. Figure 3共b兲 shows the isosurface at E = −2.76 eV which, on the other hand, corresponds to the isosurface with the lowest energy that depicts the hydrogen motion that extends on the whole surface. As the energy is further in-creased, isosurfaces at E = −2.34, −2.11, −2.04, and −2.03 eV connect the fcc hollow site to the first OH site关Fig.3共c兲兴, the first OH site to the first TH2 site关Fig.3共d兲兴, the first OH site to the second TH1 site关Fig.3共e兲兴, and the first TH2 site to the second OH site as well as the second OH site to the second TH1 site关Fig.3共f兲兴, respectively. These imply that an effective diffusion path for the hydrogen atom motion into the Pd bulk starts from the fcc hollow site on the Pd共111兲 surface. The diffusion path then passes through the
octahe-dral site between the first and the second Pd atom layers, the tetrahedral site beneath a Pd atom in the first layer共or above the Pd atom of the third layer兲, and then the octahedral site between the second and third layers. At each saddle point found in Figs. 3共c兲–3共f兲, the energy is equal to the potential energy value that defines the isosurface. In Fig. 3共c兲, for example, the potential energy value of −2.34 eV also corre-sponds to the potential energy value at the saddle point 关which in this case coincides with the midpoint of the three Pd atoms at the Pd 共111兲 surface兴 in the effective diffusion path from the fcc hollow site to the first OH site.
The isolated isosurface of −2.91 eV in Fig. 3共a兲 corre-sponds to the minimum value of the PES for the hydrogen atom motion. Figure 3共b兲 means that the hydrogen atom wave function can be distributed between the fcc and hcp hollow sites over the bridge site. In Fig.3共c兲, the isosurface between the first and second atom layers means that the hy-drogen atom is expected to have the delocalized wave func-tion from vacuum area on the surface to the first OH site with the energy level summed up by that potential energy value and any kinetic energy. In addition, the isolated isosurfaces between the second and third atom layers indicate that the hydrogen atom has the localized wave function at the first OH site with the energy level summed up by the potential energy value and the zero point energy. Similarly, Figs. 3共d兲–3共f兲 indicate the range where the hydrogen atom can distribute on the surface and in the subsurface. However, it is uncertain that these predictions are feasible without quantum calculations. The adsorption energy and the diffusion barrier should be explained in consideration of the quantum effects that the kinetic energy of the hydrogen atom becomes large when the breadth of the PES is narrow. Figure 4 shows a contour plot of the adiabatic potential energy for the hydro-gen atom motion on a cross section of the substrate cutting through the top-hcp-fcc-top site line. The breadth of the adia-batic PES for the hydrogen atom motion around the TH site is narrower than that of the OH site, and the potential energy value at the TH site is higher than that at the OH site, as shown in Figs.3 and4. To obtain the breath of the PES, the harmonic oscillation equation E共z兲=k共z−z0兲2+ D is fitted to
the potential energy curves passing through the fcc and hcp hollow sites, as shown in Fig. 1. Here, Z0 and D are the bottom position and the depth of the potential energy curve, respectively, while k corresponds to the breadth of the poten-tial energy curve. When Z0and D are adjusted for the poten-tial well centering on the first OH site and first TH site, 0.434 and 2.353 are obtained as the values of the parameter k, respectively. At other OH and TH sites, almost the same values are found. Furthermore, the parameter k along the direction parallel to the surface has similar characters as those along the z direction. Based on these features, the state of the hydrogen atom motion at the OH site can be more stable than at the TH site in considering the quantum effect due to the large kinetic energy at the TH site. Thus, the OH sites become intermediate sites in the effective diffusion path into the Pd bulk.
In the pathway from the hcp hollow site to the first TH1 site, the value of the energy barrier is 0.59 eV, while the energy barrier from the fcc site to the first OH site takes a
FIG. 2. Schematics of the specific sites of the Pd共111兲 surface and subsur-face. 共a兲 The three-dimensional 共3D兲 view, 共b兲 top view, and 共c兲 cross-sectional view cutting through the top-hcp hollow-fcc hollow-top sites of the Pd共111兲 surface. The gray spheres represent the Pd atoms, with the first, second, and third layer atoms visually represented in共b兲 with decreasing size. The small black spheres denote the specific sites: top, bridge, hcp hollow, fcc hollow, first共second兲 OH 关the octahedral site between the first and second共second and third兲 atom layers兴, first 共second兲 TH1 关the tetrahe-dral site above the second共third兲 layer Pd atom兴, and first 共second兲 TH2 关the tetrahedral site beneath the first共second兲 layer Pd atom兴.
slightly lower value at 0.57 eV. These values are the differ-ences of the potential energy values between the fcc or hcp hollow site and the saddle points of the PES, as shown in Fig.4. Hence, the diffusion path from the fcc hollow site to the first OH site has a priority in the diffusion process from the surface to the first subsurface region 共the area between the first and second atom layers兲, even if the isosurface of PES passes through the hcp hollow and first TH sites. In the case of the diffusion from the first OH site to the second OH site, there are two diffusion paths. One passes through the first OH, first TH2, and second OH sites and the other
through the second TH1 and second OH sites. The former and latter diffusion paths have almost the same priority.
Characters of the effective diffusion path from the fcc hollow site to the Pd bulk are summarized as follows: 共1兲 The effective diffusion path passes in succession
through the fcc hollow, the first OH, the first TH2, and the second OH sites, or through the fcc hollow, the first OH, the second TH1, and the second OH sites.
共2兲 The breadth of the isosurface which passes the saddle point of the PES at the three atom fold sites and between the OH and TH sites is very narrow.
FIG. 3. Three-dimensional共3D兲 views of the PES at共a兲 −2.91, 共b兲 −2.76, 共c兲 −2.34, 共d兲 −2.11, 共e兲 −2.04, and 共f兲 −2.03 eV.共a兲 The isosurface illustrat-ing the localized H atom motion at the fcc hollow site,共b兲 along the surface, 共c兲 into the first subsurface area, 共d兲 from the first OH site to the first TH2 site,共e兲 from the first OH site to the second TH1 site,共f兲 from the first TH2 site to the second OH site, and from the second TH1 site to the second OH site. Gray spheres denote Pd atoms. Circles show the points where the adiabatic PES connects.
The effective diffusion path of the hydrogen atom into the Pd bulk, as shown in Fig.5共a兲, and the PEC through the reaction path of the hydrogen atom s 共Å兲 in diffusion from the fcc hollow site on the surface to the second OH site in the subsurface, as shown in the Fig.5共b兲, are presented. Accord-ing to Fig. 5共b兲, the classical diffusion barrier from the fcc site to the first OH site is 0.57 eV, while the diffusion barrier from the first OH site to the fcc hollow site is 0.20 eV. More-over, the activation energy necessary for diffusion to the sec-ond OH site classically is 0.89 eV.
Experimental studies reveal that the initial heat of ad-sorption on Pd共111兲 is −2.85 eV.32
In our results, the adsorp-tion energy takes −2.92 eV on the fcc hollow site and this value is in good agreement with the experimental value. In addition, the diffusion barrier of the hydrogen atom from bulk Pd crystals to the surface is 0.20– 0.23 eV.33The corre-sponding value in our results is 0.42 eV, which is the diffu-sion barrier from the second OH site to the fcc hollow site, as shown in Fig. 5. Although our calculated value is larger by 0.19– 0.22 eV than the experimental data, the fact that they are of the same order of magnitude suggests that our results are plausible.
Uncertainties in the calculated values arise as notable quantum effects are expected due to the small mass of the hydrogen atom. However, if the effective diffusion path has a low potential energy value and the PES’s breadth is large at the saddle points, the hydrogen atom can diffuse in the sub-surface area easily even if the quantum effects are consid-ered. In addition, the calculated diffusion barrier may de-crease by 0.26 eV caused by the relaxation of the substrate atoms.13This is expected to affect the description of the dif-fusion mechanism of the hydrogen atom into the Pd bulk considerably. At present, the potential energy calculations
with relaxation cost a huge amount of time; hence, construc-tion of the corresponding adiabatic PES is unfeasible. How-ever, our results will be very useful to acquire the rough features of the diffusion mechanism of the hydrogen atom in the Pd surface.
IV. SUMMARY
We calculated the adiabatic potential energies for hydro-gen atom motion as part of our investigations on the behav-ior of the adsorbed hydrogen atom on the Pd共111兲 surface and in the subsurface up to the third atom layer. Our results show that the effective diffusion path of the hydrogen atom into the Pd bulk passes through the fcc hollow site on the surface and the first OH, first TH2共second TH1兲, and second OH sites in the subsurface. To quantitatively compare our results with available experimental results, we are calculating the quantum states of the hydrogen atom on the Pd共111兲 surface and in the subsurface based on this study at present. The preliminary results support the indications about the dif-fusion path and the quantum effects presented in this paper. ACKNOWLEDGMENTS
This work is partly supported by the Ministry of Educa-tion, Culture, Sports, Science and Technology of Japan 共MEXT兲, through their Special Coordination Funds for the 21st Century Center of Excellence 共COE兲 program 共G18兲
FIG. 4. Contour plot of the adiabatic potential energy surface for the hydro-gen atom motion on a cross section cutting through the top-hcp-fcc-top site line. Here, z is the distance from the Pd atomic plane of the surface first layer. x is the surface parallel coordinate along the direction through the top-hcp hollow-fcc hollow-top site line. Black and white dots denote the local minimum and the saddle points, respectively. Gray spheres and thick black lines denote the Pd atoms and the Pd atom layers, respectively. The contour spacing is 0.04 eV.
FIG. 5. 共a兲 A schematic of an effective diffusion path of a hydrogen atom into a Pd bulk.共b兲 The adiabatic potential energy curve as a function of the reaction path coordinate s, passing through the fcc hollow, first OH, first TH2, and second OH sites. The origin of s is taken from the equilibrium coordinate of the hydrogen atom at the fcc hollow site.
“Core Research and Advance Education Center for Materials Science and Nano-Engineering” and through their Grants-in-Aid for Scientific Research on Priority Areas 共Developing Next Generation Quantum Simulators and Quantum-Based Design Techniques兲, by Japan Society for the Promotion of Science共JSPS兲 through their Grants-in-Aid for Scientific Re-search 共A兲, 19206007, 2007, and by the New Energy and Industrial Technology Development Organization 共NEDO兲, through their program on “Research and Development of Polymer Electrolyte Fuel Cell Systems.” Some of the calcu-lations presented here were performed using the computer facilities of Cyber Media Center共Osaka University兲, the In-stitute of Solid State Physics共ISSP兲 Super Computer Center 共University of Tokyo兲, the Yukawa Institute 共Kyoto Univer-sity兲, and the Japan Atomic Energy Research Institute 共ITBL, JAERI兲.
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